Hero is UTG and raises AKs according to the SHC, the small blind 3-bets and we cap. We hit top pair, top kicker on the flop and the SB bets into us. How should we procede?

Many players would intuitively raise the flop or the turn, but both of these options are suboptimal.

The estimated handrange for our opponent combined with the board brings us to a way ahead – way behind situation. This means we are either way ahead and our opponent has few outs against us, or else we are far behind and have few outs. Thus, we don't know where we stand.

We can reduce the possible hands for the opposition because of his pre-flop 3-bet to the following hands: 99-AA, AK, AQ, KQ. Whereas KQ and 99 are rather unlikely since we have to give this 3-bet a lot of respect following our raise from UTG. (most opponents know that UTG raisers have, on average, better hands than raisers from, say, BU).

All these hands are either worse than our hands and have only 2 outs against us (99-QQ, KQ hat 3) or else they are better and we have 0-2 outs (AA,KK).

We don't need to protect against 2 outers and we'd be happy if they don't fold since we want them to pay us. If we are ahead, we would get the maximum by playing call flop, call turn, call river since it would not give villain a chance to fold. We also lose the minimum if we are behind because the opposition will not have a chance to reraise us. Sometimes we'll get 1SB more by raising the flop and getting called down by a pocket. However, we will lose at least 2SB more if we're behind this way and sometimes he'll fold his hand, which would also rob us of 2BB in comparison to a call from hero.
If our opponent checks, we will, of course, make a value bet.

This hand looks similar but requires a different mode of play. Here we don't get a 3-bet pre-flop. Rather, we 3-bet ourselves after an open raise from CO and our reraise was only called.

Villain's handrange, therefore, is completely different and we are not in a WAWB situation.

Hands that could beat us are almost all eliminated since we assume that KK and AA would have capped pre-flop and K5, K3 would not have been reraised.
Therefore, we will play the value line, which is often good when the following applies: we are in position, have only one opponent, have a good hand, and villain bets into us ('standard move'): call flop, raise turn.

This way you win one more small bet than if you had raised the flop.
Our opponent will usually have a bad K, which he will bet on the turn and call down if we raise.

If we are 3-bet on the turn, we should call down. In that case 55 is not unlikely, but you will be ahead often enough, for example against a K with a flush draw or some overplayed hand so that we don't need to fold without a good read of passivity. A bluff should not fold.

We have QTs and call from middle position according to the SHC. The BB raises, we call and the button limp-raises, which is unexpected but we must pay the 1 SB nonetheless.

We flop and open ended straight draw, a strong draw with 8 outs.
In another hand from the most instructive example hands from last week ( compare hands ) it was advised to raise against multiple opponents with a strong draw. Here we have a similar situation: people are already in the hand before us and there are still more to come behind us.

Still, it is correct to call here.

The arguments for a raise flop in the last hand were:

1. buying outs
We don't have an advantage here by knocking out players behind us since we can't win the hand without getting our straight anyway. After this preflop action, hitting a Q would surely not be enough to give us the best hand. We would rather keep the opposition in the hand.

2. buying the button and thereby,
a chance at a freecard on the turn
There are still 2 people behind us, one of which is a limp-raiser. It's very unlikely that both will fold, more like a 3-bet that would knock out some players; we'll never get a freecard on the turn.

3. for value:
to raise an oesd on the flop for value, we need 3 opponents to call our bets and raises. In this hand, raising runs not only the risk of a 3-bet but also that we reduce our opponent count to just 2.
-> Here it's better just to call the flop and the raise.

The turn is bad for us because full houses are no possible. In spite of this, we still have to call the donk from BB on accound of the super odds. If a raise and reraise come behind us we have to fold.

Hero hits on the river and does exactly the right thing, he calls 'for overcall'.
BB might have a hand that will beat us (A9s, 99, JJ,AA). We can be sure, however, that we are ahead of the two players who follow us (they would have given us more action with a full house).

Therefore, we call in the hope that they also call. This way we lose 2BB fewer if we are behind (otherwise we'd have to call the 3-bet from BB), but will win even more if we are ahead if they both call where they would have folded to a raise.

Hero has A2s and limps according to the SHC from middle position. The flop is perfect; we have the nut flush (only a very unlikely straight flush could beat us.
The player directly in front of us bets. Slowplay or not?
Many players are often deceived into slowplaying all their good hands. This is often a mistake since most good hands are not invulnerable, or simply because you give up value.
Here it's better to call to extract the maximum value from the hand. We hope that those behind us still call with hands that are drawing dead against us (cannot overtake us), or hands that hardly have any outs against us like small or 1 pair hands. These will gladly pay one bet, but not two.
This is only possible here because there are no hands against which we must protect.
A runner full house is unlikely enough that we would rather not drive out 1 pair hands from the flop with another bet. We don't need to protect against a straight flush either.
What about hands that could be dangerous to us?
Hands with multiple outs against us are only two pairs and sets. But these will see the river in any case, so we'd rather get the maximum value from them by raising the turn. (notwithstanding that these hands would have raised behind us on the flop anyway).

The possible straightflush on the river should not stop us from capping. Villain often just has a K or another hand that he's overplaying.